Gold Price Uncertainty, the Fix and the Quantum

Does one of the great mysteries of the universe shed light on allegations surrounding the Gold Fix? Or is it the other way around?

When Werner Heisenberg looked at his brand new quantum formulae in 1927, he noticed something weird.

The world of very small spaces and particles is ruled by matrix mechanics, but as you may remember from your school mathematics, in matrix multiplication (A * B) * C is not the same as A * (B * C). What Heisenberg saw was that because of the difference in the two matrix products there would always be uncertainty as to key physical properties of a particle. His discovery forbids a particle from having both precisely defined motion and precisely defined position at the same time.

Spotting this earned Heisenberg a Nobel prize, and a lifetime of being widely misunderstood.

The rest of us have a very deep seated 'common-sense' view of spacetime and particles, and almost all of us reject the subtle complexity of the 'Uncertainty Principle'. Indeed I am prepared to bet that if you are here reading about it for the first time you are mentally rejecting it. "Of course", you will be thinking, "whether we can measure it or not, a particle obviously has a particular position and a particular speed."

Alas you would be wrong. But don't beat yourself up about it because you are in good company. Even Albert Einstein was on your side for a while.

In physics you can pin down individual quantities very precisely, but by knowing one quantity exactly you will automatically give the particle freedom to be uncertain in another. Woe betide any physicist who interpolates between observations to state as fact something he didn't specifically measure, because physical particles do not do predictable things when they are unmeasured; they appear to spend their unobserved lives weighing up the choices of where physics allows them to be found next, and then pressing the hyperspace button to get there whenever somebody looks.

If you took to examining particle paths between observations the best route map you could draw to describe the motion of an unmeasured particle would look something like this :-

The diagram shows how we located the particle precisely at point A, and again at point B. But in being so precise about its location at an instant of time we made its motion uncertain.

At time A, it might have been going up, or down, there is no answer. In making our precise measurement of position at instant A (and B) we actually denied the particle a definitive up/down motion. It's weird, but that is how particles work in spacetime - it really is.

Nevertheless a good physicist will be able to perform certain quantum calculations, and she will be able to give us a sense of where our particle might have been found, if we had looked. She will be able to calculate that if we were to set everything up the same way and make hundreds of additional measurements at Time T, then the particle would be found in the various ranges shown on the blue dotted line on the picture, with the various probabilities shown.

Even many physicists find it unsatisfactory that the most nature allows us to say about where the particle was when we weren't looking is basically "probably about here". But there it is. Without an observation there was no single explicit position at Time T, because the phenomenon of unmeasured position did not properly exist except in our own mental models. Unmeasured position is smoothed out into a fuzzy realm of possibilities.

The Gold Fix

The situation of a particle's motion and position bears a striking similarity to price. Let's have a look at another picture.

The blue dots are 'quotes' from a market. Someone from Bloomberg has tracked bankers' gold price quotes, each of which is here represented as a blue spot.

Bloomberg decided to be helpful to the rest of us, and they filled in the gaps between the points with a solid line. Then they sold it to us as a gold price chart - a track of the position of price, through time.

A few years ago, before derivatives were invented, the rest of us would have taken that plotted line with a pinch of salt. We always knew it was an approximation, and not a very good one either, because when we waited to see the price reporting at the end of the day we could see a whole load of real gold deals (here the green dots) obstinately refusing to position themselves on Bloomberg's line.

We did not care much, because none of us who worked in real markets ever thought for one moment that anyone would start to treat the lines interpolated by Bloomberg as something real. They were a useful visualisation - that was all.

It was only later, when financial engineers started building products that were valued by reference to that line, and when people started making profits, or losing, depending on where Bloomberg drew their line, that investors started attaching significantly more weight to the line itself than to the reality of the reported deal prices.

Is the gold price uncertain too?

Okay, so I am clearly drawing a parallel. Price charts and particle route maps are doing something quite similar. But let's take it a stage further. Let's try doing what Heisenberg did, and make the bold assertion that there is no price between the data points of trades, just a realm of possibilities.

The derivatives engineers, and even a few of the gold bugs are going to go nuts with this, but it stands up to some pretty detailed scrutiny.

For a start the price that gets printed by Bloomberg is without size. If the bullion banker were to be asked a real price, by a real trader, the banker's first question would be "what is the size?" He has to know if he is quoting for a $200 deal or a $200 million dollar deal, because the prices are completely different!

This gives a third dimension to the price, one which any spot price chart always ignores. At any given point in time the price of anything is a function of the amount of it you want to buy or sell.

Unlike quantum particles this is not difficult concept to grasp. If I were a greengrocer, and you asked me for one banana, I'd probably charge you 20 pence. If you asked me for 10, I might give you a discount, and sell for £1.90 (19p each). If you asked me for 500 I might charge you a premium, because I'd have to get in the van and go and purchase a lot more bananas - so maybe £110 (22p each). But if you asked me for 1,000,000 there is no price. I don't want to sell you 1,000,000 bananas because I wouldn't know where to get them, and I certainly don't want to spend my week in the van hunting them down and paying ever larger prices for the diminishing stock! As you can see the price varies according to size.

Once you introduce this extra dimension to the price chart, so as to get the real feel for where the trading price is, the single line of Bloomberg starts to look like a gross over-simplification. Because not only is there uncertainty in the vertical momentum of the price between two measured points (trades) but also there is a completely different answer depending on the size.

So instead of a line progressing from last quote to next quote the reality is that there is a very large volume of three dimensional economic space between the points, and, with different probabilities, the next trading price could be any point within that volume.

All in all it seems to me that there is a very good case for saying that in the absence of a trade there is no such thing as price. Anyone who seeks to know a price without the hard experiment of executing a trade is deluding themselves into creating a phenomenon which does not really exist. Price is an attribute of a specific trade. It occurs meaningfully only at points in the economic continuum where an exchange happens, and it depends on the individual circumstances, reasons and emotional states of two experimenters (sorry, traders) who each foresee the price subsequently moving in opposite directions.

So price is not smoothly variable, but point-like, quantised, and a generator of uncertainty; and everything between real trades is probabilistic guesswork.

Is Gold fixed?

If I were to criticise the Gold Fix I would certainly concede that it is rather stupidly named. Also in the era of Chinese walls - rules which insist colleagues do not tell each other what their common clients are doing - there is something unusual in allowing bank principals to know their own internal customer order book.

However in my opinion this oddity is rather elegantly offset by the fact that the Gold Fix allows another bank principal to steal those orders simply by offering a better price during the auction. I believe this system is much more robust than Chinese walls, because it relies on natural competition rather than self-imposed discipline.

Also two other powerful points jump out for comment:

The Gold Fix is a real trading price. It is not a survey, like LIBOR, and it is not a chart of quotes, like the Bloomberg spot gold ticker. It is a price at which a very large number of buyers and sellers chose to deal, and this makes it real.

It was dealt in open competition in very large size, positively swamping the sizes of the individual bullion bank quotes on the Bloomberg ticker. As I explained above this size gives it a right to be different.

Besides, if the sellers thought they were getting a bad deal day after day wouldn't they simply deal on the spot market? Or on Comex? There is nothing stopping them because the Gold Fix publishes the auction prices while it is happening, and lets clients remove their orders during the process, so as to place them instead in alternative (if usually smaller) sources of liquidity.

Forgive me, but I don't really care much in any case. There remains quite a large number of people who are wedded to gold price conspiracy theories. Many of them buy paper gold (gold futures) and then grumble that sellers of paper gold exist. In my opinion they perfectly match each other's requirement!

Meanwhile not one person who has bought gold, to take delivery, has only got paper. All the sellers were able to deliver real gold. That makes a concerted price suppression story - through shorting - very difficult to swallow.

More interesting than the Gold Fix

But there is still unfinished business here, because the physics element of this story is far more interesting than the gold element. Could it be that a run-of-the-mill financial spat begins to show us a route to solving the central riddle of quantum physics? Now that really would be something.

Since quantum physics first arrived 87 years ago its application has been stupendously successful, but no-one has been able to explain its results in a way we can grasp and call 'reality'. Physicists remain stumped when it comes to describing the weird world they see through their simplest experiments.

In the absence of anything better we all fall back, a bit lazily, into the default human mental model of thinking of particles as being somewhere and moving somewhere smoothly, rather than in jerks from point to point. We have taken to thinking - much as conspiracy theorists do when they look at price charts - that unmeasured particles have real position and real motion, even when they are isolated from the rest of our universe and no-one is looking.

But this perfectly natural, common sense interpretation leaves science at an impasse. Our mental model and the experimental facts are in fundamental disagreement with each other about how stuff really is.

Physicists have been wringing their hands trying to solve this. They want to explain a reality under quantum physics in a way which does not make the act of measurement special. They want reality to be permanent, whether or not they are looking, and they have come up with some truly zany models ranging from 'there is no reality' to 'there are countless zillions of realities, and entire universes are created every nano-second to cope with all the quantum possibilities'. I am not kidding. These are both pretty standard models of quantum reality which physicists are clinging to.

Yet - and this is the amazing thing - through analysing price at the Gold Fix we can actually see a workable metaphor for quantum experiments, and that really excites me. It's as if the quantum world is an incredibly fast moving market, heaving with tiny trades, where each exchange produces an instant of perfect precision in some physical attribute or other, enabling the countless trillions of particle events in the observable universe to map themselves, with respect to each other, into the unambiguous history of our spacetime.

I have read lots of physics books, and not understood many of them, but by sitting in my office and thinking about gold prices I can for the first time start to see how something which appears to be deeply real and continuous is in fact point-like, and fuzzy between the points. I can explain, and in an understandable way to anyone who knows markets, that between one trade and the next price is undefined, uncertain and unreal. We don't know exactly where it is, or if it's moving up or down. All we can do is copy the quantum physicists and make probabilistic guesses until the next trade.

Is there something here the physicists could learn from us? After all, so many physics laboratories have lost their brightest research stars to the quant funds. Perhaps it's time the London bullion market offered the labs some of our Gold Fix dealers, on sabbatical, of course.

Paul Tustain is the founder of BullionVault.com – with 51,000 customers and $1.4bn in gold bars, now the world's largest store of privately-owned investment gold bullion.

(c) BullionVault 2014

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